Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers
The condition number for the Drazin inverse and the Drazin-inverse solution of singular linear systems \(Ax=b\) are investigated under the \(P\)-norm and a componentwise perturbation. The assumptions \(\text{Im}(E) \subseteq \text{Im}(A^k)\) and \(\text{Im}(E^T) \subseteq \text{Im}(A^k)^T\) on the perturbation \(E\) are assumed, where \(\text{Im}(E)\) denotes the range of \(E\), \(E^T\) is the transpose of \(E\) and \(k\) is the index of \(A\).
scientific article; zbMATH DE number 2184019